Fig. REF  shows the classification performance comparison of our proposed proposed Invo-ResNet with those achieved by three representative DL-based models for AMC including VGG [1]}, ResNet [1]} and MCNet [3]} on RadioML 2018.01A dataset. It is evident that the proposed Invo-ResNet is superior to other traditional models, and it can provide \(2\%\)  gains over our previous work MSNet, 2 dB gains over ResNet, 3 dB gains over MCNet and 4 dB gains over VGG. Moreover, Invo-ResNet can reach over \(90\%\)  accuracy when the SNR is larger than 6dB, and it can achieve about \(95\%\)  accuracy at 10dB, while the best performance of ResNet is \(91.47\%\)  at 10dB. To further show the superiority of the proposed Invo-ResNet, Fig. REF  illustrates the training loss during the training process of the compared models. The proposed Invo-ResNet can achieve a lower loss in the training set compared to the other models and obtains a faster convergence speed than other models. To show the effectiveness of the involution for AMC, a fully convolutional network with the same structure is trained and tested under the same dataset. As shown in Fig. REF , compared to our proposed scheme with involution, the convolutional counterpart (Conv-ResNet) only reaches a best performance of \(94.5\%\)  at high SNR condition, which is about \(1\%\)  lower than involution based model, and it performs worse than our previous work MSNet. For the analysis of the computational complexity, we calculate the network parameters of the compared models, as shown in Fig. REF . Our proposed scheme achieves a better performance with less parameters than these conventional schemes. Moreover, compared to the convolution based scheme under the same structure, our proposed scheme with involution has about \(40\%\)  reduced parameters, which can be implemented in resource limited devices.
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